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curve #4489

y² + xy = x³ − 28772x + 1126801

a-invariants: [1, 0, 0, -28772, 1126801]
c-invariants: [1381057, -975627649]
rank (lower bound): ≥ 8
torsion subgroup: trivial
conductor (N): 973533662904239
discriminant (Δ): 973533662904239
Faltings height: 1.5761
naive height: 42.4151
primes of bad reduction: 439, 24989, 88743709
regulator: 19124.4461116842004504680792754867115258848217204981876
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:31:13 UTC
last updated: 2026-10-17 10:31:13 UTC

Witness: 8 independent points log in to add more points →

(-135, 1666)
(-95, 1781)
(-49, 1580)
(-33, 1445)
(32, 473)
(37, 318)
(437, 8270)
(472, 9395)

Commentary

BASE records/rank_8.md#29 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:31:13 UTC · history

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